Computed tomography (CT) makes available a diagnostic and measurement procedure for medicine and test engineering, with the aid of which internal structures of a patient and test object can be examined, without thereby having to perform operational interventions on the patient or having to damage the test object. In this case a number of projections of the object to be examined are recorded from different angles. A 3D description of the object can be calculated from these projections.
FIG. 1 shows a typical CT arrangement with an x-ray source 1 in a first position, which transmits an x-ray beam 2 for a first projection, said beam being detected in a detector 3 at a first position, after it has penetrated the object to be examined 4. The data of the detector arrives at an evaluation computer 5 which undertakes the reconstruction, and is then displayed on a display unit 6. The x-ray source ideally moves on a circular path, with numerous projections being recorded. FIG. 1 shows by way of example the x-ray source in a different position 11, with an x-ray beam 12 being transmitted for a different projection and then being detected in the detector at a different position 13.
During the subsequent processing of the measured data it is assumed that the Lambert-Beer law
  I  =            I      0        ⁢          exp      (              -                              ∫            beam                    ⁢                                    μ              ⁡                              (                s                )                                      ⁢                          ⅆ              s                                          ⁢                          )      applies for the measured data. Here I represents the intensity measured by means of the detector 3, I0 the unattenuated intensity and μ(s) the attenuation coefficient at the location s. However, this relationship applies only for monochromatic radiation and not for the polychromatic radiation of an x-ray tube. Instead the relationship dependent on the photon energy E applies for this
  I  =            ∫              E        =        0                    E        max              ⁢                  ⁢                  ⅆ                              EI            0                    ⁡                      (            E            )                              ⁢              exp        ⁡                  (                      -                                          ∫                Beam                            ⁢                                                μ                  ⁡                                      (                                          s                      ,                      E                                        )                                                  ⁢                                                                  ⁢                                  ⅆ                  s                                                              )                    
If this dependency is not taken into account, the reconstructed image has artifacts which distort the reconstructed attenuation value by up to several percentage points (compared to a reconstruction from measured data obtained monochromatically) [Buz04].
Various methods are known in the literature for how values approximately independent of the photon energy can be calculated from the values measured in this way. The method relevant to this application is of an iterative nature and is outlined in the following.
It is first assumed that the data was recorded monochromatically. A reconstruction of the object is calculated. Then the object is segmented into different regions (for example soft tissue and bone). Several approaches are described for this in the literature. In the simplest case this can be done by means of a threshold procedure.
Artificial projections are now calculated for each tissue class from the images segmented in this way. Relevant items of information in each case are the attenuation proportion and the beam length of each x-ray beam through the segmented tissue portion.
A correction factor can be ascertained from the determined projection values and/or material thicknesses of the individual tissue classes, with which the originally measured value can be corrected, before a second, final reconstruction of the object is calculated [Cas04]. The correction procedure is illustrated diagrammatically in FIG. 2 for three different tissue classes.
Metal-like elements such as tooth implants or artificial hips create such strong artifacts that it may be that the procedure described can no longer be used. A metal artifact correction procedure is described in [Bal06] which likewise requires the calculation of different projection images through various tissue classes. In a first step those regions whose associated beams run through metal are determined on the projection image. In a second step a projection image of a model volume is determined. In the model volume metal regions are replaced by adjacent tissue classes. On the basis of both these projections the original projection values can now be corrected, so that an artifact-free image can be reconstructed. This procedure is summarized diagrammatically in FIG. 3.
The projection calculation can be performed as follows: the image is divided into rectangular pixels which in each case have the value of the attenuation coefficient at the associated scanning point across the entire pixel surface. The line integral along the beams can then be weighted as a sum of the scan values with the irradiated length through the associated pixels [Sid85]. This procedure is illustrated in FIG. 4.
Other projection algorithms are know from the literature which differ from the described method by the calculation of the weight with which a pixel is used in the projection calculation [Mue98].
In the procedures described at least two projection calculations are necessary. Furthermore, in addition to the memory for the object a further memory for the segmented objects must be kept available.